We investigate the production of invisibly decaying light scalars in association with hadronically decaying $Z$ bosons at the Future Circular Collider-ee at a centre-of-mass energy $\sqrt{s}=240$ GeV. Several new physics models predict the existence of these low-mass scalar states, while the existing experimental constraints do not yet exclude these states. We study the low-mass scalar based on a simplified extension of the Standard Model, introducing an additional scalar singlet and a scalar dark matter candidate. The analysis is performed for a set of new scalars with mass in the range $(15,120)$ GeV, by employing a selection-based strategy complemented with Multivariate Analysis techniques to discriminate the signal from background. The expected upper limits on the production cross-section times the branching fraction of the new scalars decaying invisibly are evaluated as a function of the scalar mass. We find that sensitivities of $\sim {10}^{-2}$–${10}^{-1}$~fb are achievable for scalar masses below $\sim 60$ , while sensitivities of $0.1$–$1$~fb are obtained for masses between $\sim 60$ and $120$ , with the weakest sensitivity near the $Z$-pole at scalar mass $M_S\approx 90$ . Depending on the mixing angle, novel scalars with masses below 80 as well as in the range 110–120 are within discovery reach.